DLMF:10.61.E1 (Q3790): Difference between revisions

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‎Changed an Item: Add constraint
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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 14:20, 2 January 2020

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DLMF:10.61.E1
No description defined

    Statements

    Defining formula
    ber ν ⁡ x + i ⁢ bei ν ⁡ x = J ν ⁡ ( x ⁢ e 3 ⁢ π ⁢ i / 4 ) = e ν ⁢ π ⁢ i ⁢ J ν ⁡ ( x ⁢ e - π ⁢ i / 4 ) = e ν ⁢ π ⁢ i / 2 ⁢ I ν ⁡ ( x ⁢ e π ⁢ i / 4 ) = e 3 ⁢ ν ⁢ π ⁢ i / 2 ⁢ I ν ⁡ ( x ⁢ e - 3 ⁢ π ⁢ i / 4 ) , Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Bessel-J 𝜈 𝑥 superscript 𝑒 3 𝜋 𝑖 4 superscript 𝑒 𝜈 𝜋 𝑖 Bessel-J 𝜈 𝑥 superscript 𝑒 𝜋 𝑖 4 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑥 superscript 𝑒 𝜋 𝑖 4 superscript 𝑒 3 𝜈 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑥 superscript 𝑒 3 𝜋 𝑖 4 {\displaystyle{\displaystyle\operatorname{ber}_{\nu}x+i\operatorname{bei}_{\nu% }x=J_{\nu}\left(xe^{3\pi i/4}\right)=e^{\nu\pi i}J_{\nu}\left(xe^{-\pi i/4}% \right)=e^{\nu\pi i/2}I_{\nu}\left(xe^{\pi i/4}\right)=e^{3\nu\pi i/2}I_{\nu}% \left(xe^{-3\pi i/4}\right),}}
    0 references
    DLMF id
    DLMF:10.61.E1
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    Symbols defined
    Kelvin function
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    Kelvin function
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    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
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